education

09/30/2016

I've never taken a programming class, but have done a fair amount over the years in a variety of languages. I'm not fond of it myself - at least not something I'd like to do for a living. You get spoiled being around the likes of Brian, Ken, Bjarne and Dennis -- particularly Dennis.1 I don't code seriously for the same reason I don't do serious art - I know what good is. That said knowing how to code and, just as important, how computers work, has been incredibly valuable and necessary to me over the years. Not only can I hack together what I need for physics and other purposes, but you get insight into how more complex systems behave -- sort of important these days. My belief is coding is something that young people need to be exposed to - even if they never write anything for your job. Because of this I've followed and even participated in a variety of teach-kids-to-code efforts over the years.

Most of them were awful. They tend to be implicitly and sometimes explicitly sexist. They're usually boring. Most of them don't teach you technique and many, combined with incompetent instruction, teach bad habits. CS 101 classes often have to focus on unlearning bad habits.

So why am I writing this?

Earlier today a good friend was looking for long-form reading suggestions for the weekend. Normally I have a dozen or so books that I try and push on others, but about a month ago I had a special experience. I watched a twelve year old code for the first time in her life. We, I should say she, used Swift Playgrounds - Apple's new teaching environment based on the Swift programming language. I won't get into language wars (heaven know I used to work out ideas in Common Lisp), but Swift is a very good modern programming language. Learn one well and you should be able to pick up others. What is special about Playgrounds is its playful nature. Some really serious folks who think deeply about teaching coding skills including girl gamers were involved and it shows. You start out solving a simple puzzle as it introduces concepts and you write real code. It encourages experimenting and learning from failure. It doesn't push cookie cutter solutions - you can solve an example in any number of ways, but it encourages efficient code.

She was thrilled and upset we ran out of time. I was there to help and offer suggestions, but she was off on her own. I mostly watched her excitement and thought about the enormous effort getting this as good as it is.

The full language is there and you can move your code over to Xcode and create iOS (or even OS X) apps. Educators are being encouraged to create their own games and modules with tools Apple has provided and free teacher instruction manuals are online.

Highly recommended. I can't think of a better introduction to coding. So if you know of a kid with an iPad - or if you want to learn about programming on your own - this is the real deal. All free except for the iPad ... if you don't have one, this may be is worth the price.

1 My word all of these are masters... The Picassos and Bachs of computing ... the 1 in 10,000 or 100,000 who see things so much more deeply than others. Dennis was a different sort all together - perhaps a one out of all of the programmers in the world... unique.. computing's Shakespeare.

06/13/2016

One of my most significant and hard-won learnings over the past ten years has been that conventional education is useless - even counterproductive - in combating pseudoscience in a polarized society. I've touched on it hear and a few of you have heard far too much from me. So rather than more from me here's Atul Gawande's commencement address at Caltech last Friday. For those who prefer print (I usually feel something is lost), the transcript appears in The New Yorker ..

05/19/2016

Watching a stream of the first two episodes of Genius by Stephen Hawking I was reminded of the words of one of my teenage mentors.

Awe and wonder are usually listed as synonyms, but there is an old distinction. Awe leaves you so impressed that you don't know what to do other than feel it. Wonder is deeper. You are still amazed, but now you want to understand it better. You come to learn that wonder is license to ask Nature questions for she is not unknowable.

Science education should inspire with a sense of wonder and provide a sense that paths exist. A few of the science shows, I wouldn't count Genius among them, manage this. They're expensive to produce, but there are probably lessons on making science palatable to a larger number of people. The best provide stories and even inspire a few into STEM programs. Lean-back science education. How do you get people leaning in a bit more?

I've spent a few posts on my belief the current system of American science education focuses on filling a pre-professional STEM pipeline underserving and turning off a majority of students in the process. I'd like to see something more relevant for most people.

Anton van Leeuwenhoek was a hacker - a 17th century optics hacker. A few Dutchmen perfecting glass lenses had stumbled onto the basis of compound microscopes and telescopes. Galileo heard of their work and made a telescope good enough to revolutionize astronomy and our view of our position in the Universe. Leeuwenhoek went the other direction and created the field of microscopy revolutionizing biology and our understanding of life. Little curved pieces of glass shook the foundation of our understanding of the world.

It is hard to imagine Leeuwenhoek's excitement. Almost everything he put under his microscope made him the first human to discover a bit of a tiny world that has been hiding on, among and in us. His drawings are beautiful and appear in about a hundred or so letters to the Royal Society of England. Robert Hooke was something of an English polymath. He improved on Leeuwenhock's design and, continuing the tradition of just looking at things, discovered the existence of cells. Hooke was also gifted at making accurate drawings. Biology was on its way.

Too many think of discovery as something already found and archived in textbooks or wikipedia. Real discovery is nothing like that. In fact there is still much to be discovered and some of it is very accessible. You can take delight in personal discovery. Imagine taking a scraping from your teeth to see what's there .. or perhaps see what's living on your sister's face by taking a sample with a bit of scotch tape. Real and accessible discovery.

Every kid should have at least one scientific instrument. These need to be easy enough to use, they can't get in the way of discovery, robust and portable. The idea microscope should fit in a pocket so you can look at things when you're wandering through a garden or wooded area - or perhaps your school cafeteria. Anything that allows you to see beyond your senses is a candidate, but I think microscopy is best suited for the curious kid.

I once thought that there were science haves and have-nots based on economic conditions. If you were lucky enough to be from a wealthy Western country you had a better chance of developing an interest in science than if you came from the developing world. While that may be true statistically I'm now of a different mind. I think there are those curious and not so curious people and they can be found everywhere. The trick is to get something to exercise their curiosity and it has to work equally well for everyone. It needs to work without electricity, Internet, technical sophistication and lesson plans. It has to be extraordinarily inexpensive and easy to ship across borders. It turns out just such a device exists.

Manu Prakash's group at Stanford created an origami microscope a few years ago. The Foldscope is folded from heavy printed paper for easy shipment and had a relatively sophisticated lens group. It is easy enough for an eight year old to put together and interesting enough to keep this significantly older physicist occupied. It costs about a buck to make a couple of them which make a packet. A few prototype runs have been made - there are about 50,000 of them all over the world. No real lesson plans - it is better to play and discover on your own and communicate with a growing community by Internet and physical mail.

At the moment the group is gearing up for a much larger run. I believe the deal is everyone given the opportunity to buy one has to provide a second one to someone who they think wouldn't have access to a microscope on their own. I can think of a kid in Cameroon. In the meantime wealthy Westerners can buy very nice portable field microscopes. There are a number of digital microscopes and microscope adapters for smartphones. I'd recommend against just relying on digital images - there is something very deep about observing something deeply enough to make an accurate drawing - even if you're a not-so-good artist like me.1 I'd count the ability to concentrate on something and reproduce it in the form of a sketch as one of the more powerful thinking tools I have. Most of us draw when we're little, but most of us stop and unlearn. I think you can make an argument for a basic art class like you can for math or science.

They go nearly everywhere and volunteers are translating the instruction sheet into a number of languages. I read that it takes about $25 in postage and handling to get a Foldscope into South Sudan. It is worth the cost. There are people with an interest and an ecosystem vastly different from anywhere else so it should be done. I don't know what percentage of kids and adults are curious enough to use one of these as a discovery tool, but wouldn't it be wonderful if all of the kids on the planet had one available?

Comparatively rich kids have the ability to acquire much more sophisticated instruments, but there's a rub. The "better" instruments may be too nice to take out in the field, too complex to understand well and not standard. There is an advantage to having standardized instruments at some level. That shouldn't stop anyone from spending money and looking at other classes of instruments. In fact I think there is real opportunity for building robust, easy to use scientific augmentations for smartphones.

Foldscope is a brilliant idea - lean forward science education for anyone. Of course there has to be an opportunity to discovery and play. That means unstructured and unsupervised playtime - something many children in the wealthy Western world have very little of... Too bad as the world is full of so much wonder.

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1 Lately I've decided I've taken too many snapshots and am not appreciating images so I now try to study a potential image before taking a photo - even to the point of sitting down and spending fifteen minutes sketching it to understand it a bit better.

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Recipe corner

Lumpia are sort of a spring roll from the Philippines. The term is generic - many are meat filled, some are vegetarian and they can be deep fried or roasted. Here's a variation that works well .. lots of ways to adapt!

Lumpia

Ingredients

° medium sweet potato

° 14 oz tofu firm brick

° 1/2 cup diced green beans

° 1/2 cup diced carrots

° 1 cup shredded cabbage

° 1/4 cup chopped scallions

° 3 garlic cloves chopped

° 2 tbl olive oil

° 1 tbl sesame oil

° salt and pepper

° spring roll wrappers (I'll cheat wherever I can)

Technique

° partly cook the sweet potato - throw it in the microwave for 2 or 3 minutes. Skin and chop into cubes

° drain the tofu and slice into little cubes

° put 1 tbl of olive oil in a large pan over medium-high heat. When hot add the tofu and cook until edges begin to brown. Remove tofu and set aside in a large bowl

° add the rest of the olive oil to the pan. Add garlic and cook until soft and garlicy smelling - a minute or so

05/13/2016

The other day I found myself in a school administration office arguing against a proposed expansion of an already large STEM program. STEM, if not taken to extremes, is fine. Unfortunately it has become too important in our local school displacing other important courses. It is also poorly aimed - a continuation of the pre-professional pipeline from the Cold War. Science and math are not only hugely important, but offer great beauty and delight. They should be taught in such a way that most students can come out with a background rather than a bad taste and even a distrust.

I won't have much of an impact, but that rarely stops me. I spent an hour painting a picture of how science and math might be taught. I started saying I would begin with physics - far and away the simplest of the sciences. That brought things to a halt and I had to explain. Here's roughly what I said...

The process of doing leading edge physics, like so many things, isn't simple. It can be beyond technical - measurements have to be understood to levels of accuracy that creates a steady stream of exotic instrumentation and technique. It isn't uncommon for an experimentalist to spend three quarters of her time worrying about little things that might be causing errors. A simple idea - like measuring the distance between two sets of a pair of mirrors at right angles to detect gravity waves - can consume hundreds of millions of dollars, thousands of person years of work and span four decades.1 But under all of the exotic instrumentation and mathematical technique is a very simple and direct question that gets to the heart of general relativity.

Einstein didn't have to work out the experimental details of gravity wave detection. In fact he did a quick back of the envelope calculation and came to the conclusion that the gravity wave signal would be much fainter than the noise of any practical apparatus that he wrote it was unlikely gravity waves would ever be detected. It didn't stop him from doing a thought experiment where he could ignore anything extraneous. He found the correct result. Experimental verification was impractical at the time, but very beautiful and a key to understanding Nature at a deeper level.

Einstein was famous for these gedanken - thought - experiments. He would imagine himself on a train traveling at nearly the speed of light watching signal lights at a station or on other moving trains. And wasn't just Einstein. Physics allows you to strip away the extraneous and get to the heart of the matter. That realization came with an Italian famous for dropping balls from a leaning tower and for discovering the moons of Jupiter.

Galileo Galilei was involved in at least three fundamental revolutions. Dropping balls from the Leaning Tower is probably a bit of myth from a biography by one of his students, but he did roll balls of different masses down inclined planes. He was able to show that the balls accelerated uniformly by an amount that depended on the angle of the incline. Sure the numbers weren't perfect - there was friction and air resistance - but he was smart enough to calculate how they would behave without friction or air resistance. From this he could show how any mass would behave - that a cannon ball and feather would fall at the same rate if you ignored air friction. This ability to focus on the core issue and account for the distractions was one of the biggest revolutions in history. The moons of Jupiter were a big deal too, but not for the moment.

The other sciences are messier - you have to account for many effects that are difficult, often impossible, to control or ignore. Great progress has been made, but it is difficult and often impossible to ask questions at the fundamental level you can get to in physics. As systems become very complex - life for example - serious problems with the quality of work exist. There are brilliant people in these areas and they do the best they can - its just their domain is far from simple. Physicists have it easy.

Galileo was part of a chain of one of the most important threads of deeply understanding Nature - the conservation of momentum. Aristotle created a physics that was more of a teleology than a science. He applied common sense to observation and said everything had some natural state and that any process had to have a goal. You may have encountered his four causes in a philosophy class - I won't go into them as they're confusing to us now. To get something moving we have to push. To keep it moving he would have us keep pushing it. Everything in motion is being moved. Everything changing is being changed.

Galileo was a central part of a five hundred year effort that lead towards understanding momentum and simplification was a critical step as the deep understanding appeared.2 If something is in motion it will stay in motion if you don't make any changes - friction can slow it down and stop it. Aristotle had to have a mover - something that led to a motion or any other change - like the sound of a bird or the change of color of fading paint. Each of these properties had to have some kind of cause.

Along comes the conservation of momentum and the Universe doesn't need these constant pushes - it just keeps going. This is a fundamental shift in how we see reality - every bit as important as moving from a world centered universe to a heliocentric universe to the centerless universe. We've also moved to quantum physics where the concepts of absolute causes and effects are foreign. That gift of Nature that Galileo showed so beautiful - the ability to simplify the basic questions. This allowed a chain of events that have given us so much of our current world.

So many of the basic concepts, in the hands of good teacher, can be taught clearly. I didn't manage to get started on storytelling, naturalism and beauty... all areas appropriate for high school and understanding the world For most there isn't a need to calculate or memorize. The same holds for chemistry and biology and the mixtures and combinations. Of course this won't happen, but it is nice to dream and to attempt to get administrators to think a bit. .

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1 It isn't the rule, but sometimes you can build a very simple experiment and make a real discovery. James Chadwick built a simple apparatus to discover the neutron .. a feat that took about two weeks and won a Nobel Prize. Sealing wax was involved.

2 This is a fun area to explore moving from Persia to Europe. Galileo almost got momentum right - and he named it. Christiaan Huygens nailed it and, of course, that singularly Newton integrated it into his laws of motion.

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Recipe corner

Early rhubarb is out. It isn't the rich red you think of when you think rhubarb, but there's nothing wrong with it other than price. I couldn't wait and ended up trying an experiment that worked out well. Try roasting it. Trim off the leaves as you always should with rhubarb (the leaves are mildly toxic) and chop into convenient roasting size (about two inches in my book). Coat them with a mixture of butter and sugar and roast in a 400°F (200° - 210°C ) over for about 15 minutes. It is wonderful! I used demerara sugar on a second batch to bring out more of a molasses flavor. Even more wonderful. The next trick is to use this in place of strawberries (I'm allergic) in a strawberry shortcake recipe. It should work well.

04/16/2016

Canada is undergoing a fantastic profound change. For more than a decade the government has chosen to underfund science, undermine Universities and science education and focus on a path of applied paths that are somehow guaranteed payoff. This changed with the last election. Prime Minister Justin Trudeau shows a genuine interest in science and technology and the support is beginning to be felt in the trenches. This seems to have captured everyone's attention.

Reflecting on it left me a bit depressed. A government official, asked about a major bit of spending, is expected to provide answers to a press that knows what questions to ask -- except, in the US at least, in science and math. Somehow it is ok to be ignorant. For people in power there is an army of people ready to provide a mini education on the main points. I doubt Trudeau knows anything about Shor's algorithm, but he probably has the time to learn about the science and technology, where things might go and where it makes sense to provide some help.

In the US we have a press and political class that often focuses on pseudoscience as much as it does science. Part of the blame is education. There are a few champions who have been trying to change that. Carl Sagan was undoubtedly one of the most important popularizers. He wrote extensively on the value of science and the harm of pseudoscience - perhaps best in The Demon Haunted World. A few bits (my copy is very dog-eared and marked up)

Superstition and pseudoscience keep getting in the way, distracting [believers in pseudoscience], providing easy answers, dodging skeptical scrutiny, casually pressing our awe buttons and cheapening the experience, making us routine and comfortable practitioners as well as victims of credulity. Yes, the world would be a more interesting place if there were UFOs lurking in the deep waters off Bermuda and eating ships and planes, or if dead people could take control of our hands and writers messages. It would be fascinating if adolescents were able to make telephone handsets rocket off their cradles just by thinking at them or if our dreams could, more often than can be explained by chance and our knowledge of the world, actually foretell the future. These are all instances of pseudoscience. They purport to use the methods and findings of science, while in fact they are faithless to its nature-often because they are based on insufficient evidence or because they ignore clues that point the other way. They ripple with gullibility.

....

Pseudoscience is easier to contrive than science, because distracting confrontations with reality–where we cannot control the outcome of the comparison–are more readily avoided. The standards of argument, what passes for evidence, are much more relaxed. In part for the same reasons, it is much easier to present pseudoscience to the general public than science.

At the heart of some pseudoscience is the idea that wishing makes it so. How satisfying it would be, as in folklore and children’s stories, to fulfill our hearts desire just by wishing. How seductive this notion is, especially when compared with the hard work and good luck usually required to achieve our hopes.

...

Pseudoscience differs from erroneous science. Science thrives on errors, cutting them away one by one. False conclusions are drawn all the time, but they are drawn tentatively. Hypotheses are framed so they are capable of being disproved. A succession of alternative hypotheses is confronted by experiment and observation. Science gropes and staggers toward improved understanding. Proprietary feelings are of course offended when a scientific hypothesis is disproved, but such disproofs are recognized as central to the scientific enterprise. Pseudoscience is just the opposite. Hypotheses are often framed precisely so they are invulnerable to any experiment that offers a prospect of disproof, so even in principle they cannot be invalidated. Practitioners are defensive and wary. Skeptical scrutiny is opposed. When the pseudoscientific hypothesis fails to catch fire with scientists, conspiracies to suppress it are deduced.

....

It is a supreme challenge for the popularizer of science to make clear the actual, tortuous history of its great discoveries and the misapprehensions and occasional stubborn refusal by its practitioners to change course. Many, perhaps most, science textbooks for budding scientists tread lightly here. It is enormously easier to present in an appealing way the wisdom distilled from centuries of patient and collective interrogation of nature than to detail the messy distillation apparatus. The method of science, as stodgy and grumpy as it may seem, is far more important than the findings of science.

That leaves the task of communicating science. Something I have struggled with for a long time. Einstein often said that the mark of knowing your stuff is being able to communicate it to an interested person who doesn't have your background.1 Defending my Ph.D. thesis was, as it is for most people, straightforward and without surprises. The surprise was a requirement to communicate what I did to a high school physics class. I still have nightmares. What a disaster. My advisor stepped in and saved the day getting to the core without jargon. He took a few liberties with physics getting there, but the core idea came through and stood alone.

I still try. Sometimes with this blog and sometimes just walking with someone. Walking is much easier (assuming someone can save you from the traffic - eh Juliette?) as it is a give an take. Trying to communicate an idea with someone where you have feedback can be an exhilarating experience and often you learn something. If you're really lucky you can learn from them about their area of expertise.

Part of the trick is avoiding jargon and finding an accurate nugget. Extra points if it is visual or poetic (Sagan was very poetic). When I get in the muck trying to work out a path I remember a story by Richard Feynman:2

We used to go up to the Catskill Mountains for vacations. In New York, you go the Catskill Mountains for vacations. The poor husbands had to go to work during the week, but they would come rushing out for weekends and stay with their families. On the weekends, my father would take me for walks in the woods. He often took me for walks, and we learned all about nature, and so an, in the process. But the other children, friends of mine also wanted to go, and tried to get my father to take them. He didn't want to, because he said I was more advanced. I'm not trying to tell you how to teach, because what my father was doing was with a class of just one student; if he had a class of more than one, he was incapable of doing it.

So we went alone for our walk in the woods. But mothers were very powerful in those day's as they are now, and they convinced the other fathers that they had to take their own sons out for walks in the woods. So all fathers took all sons out for walks in the woods one Sunday afternoon. The next day, Monday, we were playing in the fields and this boy said to me, "See that bird standing on the stump there? What's the name of it?"

I said, "I haven't got the slightest idea." He said, 'It’s a brown-throated thrush. Your father doesn't teach you much about science."

I smiled to myself, because my father had already taught me that [the name] doesn't tell me anything about the bird. He taught me "See that bird? It's a brown-throated thrush, but in Germany it's called a halsenflugel, and in Chinese they call it a chung ling and even if you know all those names for it, you still know nothing about the bird--you only know something about people; what they call that bird. Now that thrush sings, and teaches its young to fly, and flies so many miles away during the summer across the country, and nobody knows how it finds its way," and so forth. There is a difference between the name of the thing and what goes on.

The result of this is that I cannot remember anybody's name, and when people discuss physics with me they often are exasperated when they say "the Fitz-Cronin effect," and I ask "What is the effect?" and I can't remember the name.

I would like to say a word or two--may I interrupt my little tale--about words and definitions, because it is necessary to learn the words.

It is not science. That doesn't mean, just because it is not science, that we don't have to teach the words. We are not talking about what to teach; we are talking about what science is. It is not science to know how to change Centigrade to Fahrenheit. It's necessary, but it is not exactly science. In the same sense, if you were discussing what art is, you wouldn't say art is the knowledge of the fact that a 3-B pencil is softer than a 2-H pencil. It's a distinct difference. That doesn't mean an art teacher shouldn't teach that, or that an artist gets along very well if he doesn't know that.

In order to talk to each other, we have to have words, and that's all right. It's a good idea to try to see the difference, and it's a good idea to know when we are teaching the tools of science, such as words, and when we are teaching science itself.

It takes me back to my high school biology class.Mostly rote memorization and very little science. Looking back there were many fascinating concepts, but I had no clue they might be interesting as I slogged through mnemonic memory tricks the teacher provided so we could make it through the multiple choice and fill-in-the-blank tests. Other than the thrill of some semi-dangerous experiments, chemistry class wasn't much better. In the end you could sound like you knew something, but it was just a veneer. It would be much better to teach real concepts and forget about the terminology. Fortunately some classes have moved in that direction.

You also need to be able to build a pseudoscience detector. Science is great at bull-sh*t detection, but it can take time and is often not presented well. But here's a nice trick that trips up many of the pseudo-science crowd - the people who try to sound smart but don't really say anything (Deepak Chopra comes to mind). Again from Feynman:

I finally figured out a way to test whether you have taught an idea or you have only taught a definition. Test it this way: You say, 'Without using the new word which you have just learned, try to rephrase what you have just learned in your own language. Without using the word 'energy', tell me what you know now about the dog's motion.' You cannot. So you learned nothing about science.

If a specialist can't express something in clear language to a non-specialist they have no business explaining it in the first place. If you hear someone rambling on, stop them and ask them to express it non-technically without the jargon. If you ask them about something they can't find language for, and there are some ideas that fit that category, they should tell you they can't explain it clearly. Feynman was very frank upfront.

I struggle along and beg your patience. Fortunately there are people who are very skilled at the sport often using visual tools and other approaches that are much more effective than my rambling. But I'll try and sometimes I'm not bad in small groups or one on one. It is a most worthy challenge. After all, there are many intersections of clarity and accuracy. Being clever enough to create and present the right one for an audience is the trick.

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1 While he did write a clear book on relatively aimed at high school students, it is not terribly accessible unless you have a firm understanding of high school math .. If you are motivated to learn and remember high school trig by all means go for it, but thee are some excellent texts that have appeared over the years that do at better job at high school and college levels. For brief overviews others have provided clearer explanations that aren't rigorous .. you won't understand special relativity reading or watching them, but you'll have a pretty good idea of what it is and why it was revolutionary.

2 From the talk What is Science from the annual meeting of the National Science Teachers Association in 1966. It was reprinted in The Physics Teacher Vol. 7, issue 6, 1968

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Recipe Corner..

Just a quick trick. I have a good friend with West African heritage and tried to make a few dishes of the area. Completely non-authentic, but many of the soups and stews have peanuts. That turns out to be brilliant. If you're making a vegetable soup with the standards - onions, carrots, celery and tomatoes - try throwing it a couple of tablespoons of peanut butter for each serving and a handful of chopped peanuts. The resulting soup is very rich and has much more protein than the vegetable base.

04/03/2016

About twenty years ago Mattel rolled out Teen Talk Barbie - a talking Barbie that had 270 phrases. One of them turned out to be controversial and the doll disappeared from the shelves to be replaced by one with 269:

The remake was warranted, but sadly many Americans agreed with what she was saying and helped instill the sentiment in their children. Americans tend to believe math is hard and that you need special gifts to do it well. They also see it as little more than a tool. An exceedingly unfriendly tool.

A few friends mentioned Andrew Hacker's book on math education was wrong to the point of being clueless. I had come across a few of his newspaper op-eds that were enough to keep me away, but last week Evelyn Lamb, a math postdoc at the U of Utah, published a great commentary in Slate.

I've only taught in universities and can't claim to be a professional teacher. Some of you are and have a much better sense of challenges and direction, so consider what I say nothing more than opinion from someone who went deep on the science and math track years ago. It may seen odd, but I worry that STEM education is gets too much attention and, in its current form, is poorly tuned to the needs of most students and society. I've commented on my belief that those who will go on into technical areas are already well served.1 Science and math courses need to be taught so as to engage and even inspire more of the students. We need to move from the pre-professional track that excludes most students to something that engages most students. We can't have people nodding their heads thinking Barbie was onto something.

Math is in particular need of re-work. There is too much repetition, memorization and mechanical effort. Math has a beauty of its own - a beauty that can be taught at many levels. Kids can worry about puzzles, knots, various types of infinity, probability, risk analysis, and dozens of other areas without touching on trains traveling from Cleveland at 47mph. Interdisciplinary work is obvious - probability fits in with sports, biology, history, science and many other subjects. Here's an example that might appeal to young bike riders - the math could easily be worked out by high school students. The fact it took a real mathematician to work on it is commentary on how many interesting questions there are rather than the problem being difficult.

Beyond the useful there is the beauty of the subject. It really needs to be considered on a level with art and music and not just a tool. There are simple ways that can bring flashes of insight .. You may have seen the construction attributed to Archimedes that seems to indicate the circumference of a circle is 4 rather than π. Of course this is wrong, but understanding why and gets you into a class of beautiful objects. I remember being enthralled with them when I discovered them in an article by Martin Gardner in Scientific American. Here Vi Hart encourages students to dip their toes in the subject:

Unfortunately a good deal of the STEM curriculum was written by technical types who work towards the preprofessional pipelines. One is reminded of buying parachutes designed by birds - maybe for those who will grind it through to become experts, but everyone else gets killed along the way. We've seen this type of panic over job relevant skills before.2 The notion of relevant STEM is fine, but it needs to engage and inspire most students on one hand and isn't watered down like Hacker suggests on the other. Students need to realize there are many dots to connect and having played with dot connection a bit first seems right and math is a big fundamental dot that has connections, both obvious and subtle, nearly everywhere.

Evelyn, the young mathematician who took on Andrew Hacker, came to her passion as an undergraduate and is fascinated by the mathematics of sewing (among other things). It turns out to be deep .. she notes:

When you get down to it, sewing is applied geometry. You are using flat pieces of fabric to approximate the curvature of a complicated surface. Seamstresses and other sewists don’t get much credit for their research in applied geometry, perhaps because traditionally "feminine” activities are not assumed to be very mathematical. Of course, those of us who sew or make crocheted hyperbolic planes or Klein quartic curves know better!

Barbie indeed

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1 There is a good deal of underemployment in many of the sciences - far too many Ph.D.s, often brilliant, for each position.

2 So many stories here. One of the funniest was a group of universities trying to mandate computer literacy by mandating APL classes for the entire freshman class. This was in the mid 70s and fortunately crashed and burned before the end of the first semester. A friend who happens to be one of the great computer scientists of the world has taught introductory CS courses and notes kids who had a high school background often come with bad habits that are difficult to unlearn. The kids who do best are those who had a bit of logic and probability in high school. Also music students did very well.

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Recipe corner

Spring has finally arrived! Here's a quick linquine

Spring Asparagus Linguine

Ingredients

° 12 oz linguine

° 1/3 c olive oil

° 1/4 cup of nuts - pine nuts are traditional, I used pecan bits

° 4 garlic cloves sliced

° 2 pounds of asparagus, trimmed and cut into inchish pieces

° salt and pepper

° 2-3 oz shaved parmesan (omit if vegan)

Technique

° cook the pasta according to directions on the box, drain and return to pot

° heat the olive oil in a skillet over medium heat. Add the nuts and garlic and cook for a minute or two - don't overcook. Add the asparagus and cook 'til tender .. 2 or 3 minutes.

° add the asparagus+nuts to the linguine with some salt and pepper and toss. Sprinkle with the cheese if you like and serve

03/08/2016

Judging a regional science fair year ago I noticed two types of kids. Most were on a pre-professional/get into a good college track. Many were interning in real labs. Great experience, but very few had any depth. Then there were the kids who were working on projects of their own. This was a regional science fair and most of the low quality entrants had been weeded out. Some of these homebrew types reminded me of C.L. Strong's Amateur ScientistScientific American column that ran during the 50s and 60s. These were seriously motivated kids.

The project that grabbed my attention was more technology and experimental apparatus than science experiment. Somehow his assigned mentor signed him off as 'safe'. I was charged with the final safety inspections the first morning of the fair. His homemade electron microscope had severely dangerous wiring - it would be fairly easy to kill yourself. I asked him how he would bring it to ground and watched him demonstrate placing a large screwdriver blade across two exposed contacts less than an inch apart. yikes! But at the same time it was beautiful. He had solved a number of engineering and design challenges - the vacuum system was clever and showed a good practical working knowledge. Except for the high voltage electronics I would have been impressed had he been a grad student.

During my ten years of judging I only had to disqualify two out of perhaps five or six hundred projects. But he was displaying passion and something had to be done. I brought over two judges from Bell Labs and got him to power it up (under supervision!) for a demo. The damn thing worked and produced beautiful images. The next week the 11th grader was contacted by professors at MIT, CMU and Berkeley with offers to come and visit. He accepted an offer to MIT during his visit there and was spared the hassle of applying. Later I learned he went on from there and is now a researcher building atomic fountain clocks at NIST. His is an extreme example, but you have to love people who are visited with the motivation to build rather than buy.

A reader wanted a digital microscope recommendation for his 11 year old daughter. I love the idea of kids and microscopes. Playing in and with Nature is great. Play where you remove some of the constraints our senses impose makes for an even richer experience. While there are many cheap digital microscopes on the market, I'd recommend something that attaches to a smartphone as you can take and analyze photos using what is an excellent camera with part of a good optical train. There are a few you can buy, but why not start by making your own?

I'm answering in the form of a post as it might be interesting to others who know kids or may happen to be one. It is possible to use a simple lens and project onto a smartphone lens. All you need to do is figure out some way to hold it and the sample at the right distances. You could do this with an ice lens, but that is better left to starting fires. Glass beads work - a few years ago I built one for an iPhone that produced remarkably clear images - I had to go through a half dozen glass beads to find a good one, but still... It wasn't very user friendly, but that may be inspiration for making one that is.

Here's a very simple 'scope making use of the lens in a laser pointer - you have to love the lens holder.

and a 3d printed glass bead holder/smartphone adapter from Pacific Northwest National Laboratory - the file is free. You can print it at your school, some public libraries or just send the file to a printing company - I can't say I'd recommend buying your own printer at this point unless you are seriously into design and prototyping.

Once they've learned about microscopy perhaps they'll get excited... at that point perhaps something more robust with better optics makes sense. I've borrowed a Bodelin adapter that was great for walking into the woods to see Nature at a different scale. Then again perhaps she could design her own..

_________

Recipe Corner

a few weeks ago Gregg V asked for my chili recipe. For what its worth this one isn't bad and, like many chili recipes, is very tolerant to variation..

rather than type it in, I'll add what I sent to Gregg:

Here’s the base recipe I use for the chili … someone sent it to me years ago and I only follow it roughly. In the Winter sticking to canned veggies usually wins .. particularly for tomatoes. I also used canned beans for this as it is thrown together on snowy days.. all cans are the 12-15 oz size here. On beans just throw in whatever you want. I usually go mostly black and pinto, but pick one, all or off the list… On the peppers usually do two red and one green,, the author was going for color. It is way better if you stew plum tomatoes down into a sauce unless you have a great store bought sauce - I haven’t found a good plain one, but in a pinch its ok. The masa/cornmeal addition is the trick. I also usually go for 2 c of broth and 1 of beer (Sukie has the rest:-) Of course the chili powder section is where you may want to go wilder, but this is a good basic filling chili

In a large pot, heat the oil over medium heat. Add the garlic, onion, 3 colors of bell pepper, carrots, celery, and jalapeno, then cook for about 5 minutes, stirring occasionally, until starting to soften. Add the oregano, cumin, chili powder, and salt. Stir and cook for a few more minutes.

Pour in the broth, tomato sauce, and tomato + chiles. Stir, bring to a boil, then reduce the heat to low, cover, and simmer for 30 minutes. Add the beans, stir, then cover and simmer for 30 more minutes.

Mix the masa with the warm water and stir it into the pot. Simmer for 15 more minutes. Taste and adjust seasonings.

02/29/2016

During the thirties Earnest Lawrence and a few others invented big science. Really big, government funded science. Science on a scale larger than organizations like Bell Labs or Universities could muster. Most of this was in the form of applied science and research engineering that bore fruit in WWII. It was recognized that pure research was a serendipity machine, so that was supported at unprecedented levels. The fly in the ointment was not having enough scientists, engineers and mathematicians...

The solution was to create a science and math pipeline not unlike the pipelines for the NFL and NBA. Beginning around the fifth grade and continuing through grad school the focus was on the small percentage of kids who would become scientists and engineers. MIT and Stanford were responsible for creating high school physics curriculum - my high school used the MIT flavor. Math buckled down taking a leap beyond its traditional 19th century K12 calculation focus. Teachers and parents revolted against the math curriculum restoring 'old' math, but the science path was successful. A secure physics Ph.D. pipeline was built and coming up to speed. Pipelines had been created for most of science and engineering. They continue to accomplish their goal (sort of). America still produces world class scientists. At the same time we have a society with disturbingly low science and math literacy. What gives?

My belief, and I stress that I'm not an educator, is that there is far to much focus on the pre-professional pipeline. Science and math classes are boring to the majority of students. Advanced classes are designed to equal first year college courses, but many beginning science courses have to be remedial. This, at a time when science and technology issues are taking central stage. Citizens should know how to judge claims of all types. They should have enough logic and critical analysis to grapple with change. We need to tie together learnings from several backgrounds. We need a different direction.

slöjd (sloyd education in America)

There are those times when you're having a conversation and a word eludes only reappearing at some useless time. Last week I was having a fine discussion with Gregg V and couldn't remember slöjd. As is often the case it showed up much later when I was thinking about something else. Just a few minutes ago, in fact.

A few weeks ago I met with the local school system about their STEM program. While I'm a fan of science and math, I worry about the current obsession with STEM über alles. A student should learn how to learn, how to apply learning to the real work, how and why to be skeptical, how to be creative and so on. Much of the STEM programs I've seen aren't terribly different from those that have existed since the fifties and Sputnik - aimed at keeping a pipeline working, this time for businesses that need these skills. It has become a 21st century vo-tec.

I asked about their once wonderful shop facility. It turns out shop and home economics disappeared two decades ago. Oddly one of the problems physics grad schools have is many students don't know how to build anything now. An experimentalist is expected to have excellent experience with any number of engineering fields plus an ability to make. At the time I brought up slöjd - part of the Scandinavian education program since the mid 1800s. It is usually described as crafting. In American system part of it was brought over and morphed into a vocational system. A system that has largely disappeared.

A student is to learn how to design and create products and art out of different materials - In Denmark that means proficiency in wood, metal and textiles. Learning how to use tools and increase making and designing capabilities as the student matures. A goal is to build an appreciation for good design and culture. Art is connected to history to design to materials and engineering - not on every project, but a groundwork is created to appreciate the art of dot-connection. It is telling that Iceland, in the wake of their banking collapse, saw the creation of about two dozen small fashion labels - a few of them good. The average Icelander knows a bit about design, craft and textiles.

I'd love to see schools teach design and making. Perhaps the objects aren't immediately useful, but the lessons may prove much more useful. I still find lessons from my 8th grade art class valuable - perhaps more than any other class in took in junior high (middle) school.

My public education was good in the sense that I wasn't over scheduled and had enough time to think. There wasn't too much homework and I had found some side projects and mentors that made an enormous difference. In high school I had two wonderful teachers - Joe Wolff and Beverly Boe. Mr Wolff taught world history and the history of religion. Ms Boe taught American history. Neither of them believed in teaching dates and facts, but taught context and how to ask questions. Two of the finest teachers I've ever had - I was lucky.

Beyond bringing back some form of making and design I have a few ideas for science, math and computing. I won't dwell on math or programming now, but a few notes on science.1

I'd like to see the Cold War pre-professional science pipeline broken up. We have more than enough scientists and it happens many of us found our own way in. Instilling an interest is much more important than 'learning' how to do it. In fact you really don't learn how to do science until you are in grad school and it is possible for a curious kid with zero background to start off in a good science program and do just as well as those who have had all of the AP classes - sometimes better.

There are ways of looking at the world that can be learned qualitatively and semi-quantitatively. This leaves the non-pre-professional student with a much deeper appreciation rather than worrying about memorizing the right formula and trying to guess when it is applicable. It is not unlike teaching a love of physical activity in high school rather than concentrating on building a great football team. I'd start off with the most basic and simple of the sciences - physics - in the eighth or ninth grade. For starters imagine answering a few questions curious kids might have that are rich in science. A few of my teenage questions:

why does sound seem to travel further on a cold day?

why is the space between double rainbows dark and why is the color order mirrored?

why is water a liquid at room temperature when other simple light molecules are gases? (this one turns out to be central to sorting out the quackery of homeopathy)

Water turns out to be a rich area - why do ponds freeze at the top and not at the bottom?

why are trains so efficient?

how do trains stay on the rails and go around curves?

why isn't the sky as bright as the Sun at night if there are so many stars in the Universe?

why do rivers meander?

how do the tides work?

why did pirates wear an eye patch? (there is some basic biochemistry in this one too)

why do mirrors flip from left to right, but not up to down?

should you run or walk in the rain?

how do ice skates work? (ok - this one is still unsettled)

what does it really mean to say a pot of water is boiling?

...

A good deal of very interesting 20th physics can be explained at a very general level. Learning a bit about the different types and risks of radiation is much more useful to the average citizen than calculating the period of a pendulum over and over. Even quantum mechanics and some of the wonderful discoveries about the universe are accessible at a public level and become dots for future connection for those who learn about them.

All of this should be taught in the context of today's understanding as well as the history and culture discoveries were made. It is much better to focus on a few small stories rather than to attempt a broad perspective. The point is to make it interesting and connected.

Chemistry is the next level of complexity and approaching it after a year of qualitative physics seems like a good approach. At this point some simple calculations can enter. Learning how to make and understand measurements would be a focus - particularly as sensor festooned smartphones and other personal devices become more common. We need to understand the environment we're measuring.

Biology is the most complex of the basic sciences and would come in the 11th grade. Understanding systems in context is critically important. Grocking the basics like natural selection rather than mindlessly memorizing the Krebs cycle. Perhaps learning about our own bodies and the impact of nutrition, exercise, sleep, and so on. A historical approach is useful as much of the country still doesn't understand evolution and we're at a point where the public meets CRISPR. (yikes!)

For the senior year there might be cross disciplinary courses with a focus on critical thinking, connecting the dots and creativity in general. Perhaps focusing on two or three major topics. I'd nominate global warming, the ethics of technology and critically evaluating medical and advertising claims. The focus is not the pipeline, but rather the educated student.

Lots of bad things to say about the quantified student, using big data to create individual education programs, high frequency and rote testing, over scheduling, etc. etc. Lots of good things about lean forward rather than backward learning.

Of course what I say and three dollars won't get you a good cup of coffee... All of us have ideas about education - feel free to comment or chat about yours and what you like/dislike about mine.

__________

1 I'm impressed with the mechanics of the Kahn Academy, but they're barking up the wrong 19th century tree. We need to teach real math. Much more to say, but later ... A friend who has taught many entry level programming courses notes that a very large number of kids come in with bad habits. There are some more interesting approaches than the current defaults - again, not aiming at the pipeline.

__________

Recipe corner

A very simple way to create a lot of caramelized onions that will store and be useful in many recipes The amounts and exact ratios are very non-critical.

12/31/2015

I’ve had a number of fine surprises this year, but Piper Harron’s PhD thesis in number theory is at or near the top. Why takes a bit of explaining.

Math is core to almost everything we do, but sadly it has become abstracted for too many people. Part of the blame falls on the mathematicians. The failure rate of math undergrads in many schools is very high. You come into realizing how little you know, but often bootstrapping is too difficult. Some of its fields have become exceptionally technical. No one in their right mind would do a PhD thesis in number theory unless they were extremely brilliant as the “good” problem space has become the territory of genius. These departments have become formidable ivory towers.

So along comes Piper - a young woman with an interest in number theory who understands math for what it is - a deeply cultural and human undertaking. After all, you have to convince others that your proofs work - something that is seriously broken these days (the abc conjecture in number theory comes to mind as do any number of computational proofs).

Her thesis is *very* readable and pedagogical. A sophomore math or physics major should be able to grab enough of a hold to bootstrap themselves through with a bit of work. A senior level student should find it a delight. There aren’t many math thesis that grab you. I was sent a copy on Christmas Eve day and its style drew me in. It isn’t a terribly deep result, but it is different from conventional math papers in the sense that Minute Physics or Physics Girl are different from physics for high school students and college non-majors. I’ll hazard a guess that it will be widely read and will have a greater impact than any other math thesis this year - perhaps this decade.

Some of you have serious math skills, others have studied other areas with not much exposure. If you know math jump it, otherwise just read the part I quote and perhaps skim the paper for cartoons and structure … the point is not so much to read the paper as to understand what she is doing culturally.

Maybe, just maybe, math and math education is changing and becoming less elite. That is exciting.

Respected research math is dominated by men of a certain attitude. Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success. As any good grad student would do, I tried to fit in, mathematically. I absorbed the atmosphere and took attitudes to heart. I was miserable, and on the verge of failure. The problem was not individuals, but a system of self-preservation that, from the outside, feels like a long string of betrayals, some big, some small, perpetrated by your only support system. When I physically removed myself from the situation, I did not know where I was or what to do. First thought: FREEDOM!!!! Second thought: but what about the others like me, who don’t do math the “right way” but could still greatly contribute to the community? I combined those two thoughts and started from zero on my thesis. What resulted was a thesis written for those who do not feel that they are encouraged to be themselves. People who, for instance, try to read a math paper and think, “Oh my goodness what on earth does any of this mean why can’t they just say what they mean????” rather than, “Ah, what lovely results!” (I can’t even pretend to know how “normal” mathematicians feel when they read math, but I know it’s not how I feel.) My thesis is, in many ways, not very serious, sometimes sarcastic, brutally honest, and very me. It is my art. It is myself. It is also as mathematically complete as I could honestly make it.

I’m unwilling to pretend that all manner of ways of thinking are equally encouraged, or that there aren’t very real issues of lack of diversity. It is not my place to make the system comfortable with itself. This may be challenging for happy mathematicians to read through; my only hope is that the challenge is accepted.

Chapter 1

Introduction

1.1 Notes to My Dear Reader(s) 1.1.1 The Layperson: Math 101

I will always be honest with you.

The hardest part about math is the level of abstraction required. We have innate logical abilities, but they are based in context. If you give people a scenario of university students drinking beverages at a bar and give them information either about the person’s age or about the person’s beverage, most people know instinctively which students’ drinks or IDs need to be checked to avoid underaged drinking (i.e., if the person’s 22 you don’t care what they’re drinking, but if the person has a vodka tonic, you need to know their age). Take the logically equivalent situation of cards with a color on one side and a number on the other. Suddenly it takes some work to figure out which cards have to be turned over to satisfy a given condition (say, all even numbers have red on the back). Just one level of abstraction and the untrained, but educated, person will have a good amount of difficulty even understanding the situation. Now try doing Number Theory.

I like to imagine abstraction (abstractly ha ha ha) as pulling the strings on a marionette. The marionette, being “real life,” is easily accessible. Everyone understands the marionette whether it’s walking or dancing or fighting. We can see it and it makes sense. But watch instead the hands of the puppeteers. Can you look at the hand movements of the puppeteers and know what the marionette is doing? A puppeteer walks up to you and says “I’m really excited about figuring out Fermat’s Last Thumb Bend!” You say, “huh?” The puppeteer responds, “Oh, well, it’s simply a matter of realizing that the main thumb joint has several properties that distinguish it from...” You’re already starting to fantasize about the Zombie Apocalypse. Imagine it gets worse. Much, much worse. Imagine that the marionettes we see are controlled by marionettoids we don’t see which are in turn controlled by pre-puppeteers which are finally controlled by actual puppeteers. NEVER HAVE A CONVERSATION WITH THESE FICTIONAL ACTUAL PUPPETEERS ABOUT THEIR WORK!

I spent years trying to fake puppeteer lingo, but I have officially given up. My goal here is to write something that I can understand and remember and talk about with my non-puppeteer friends and family, which will allow me to speak my own language to the puppeteers. To you, the lay reader, I recommend reading this introduction and then starting each subsection of laysplanations (the .1s) and reading until you hit your mathiness threshold (stopping to think or write something down is encouraged; even math you know won’t necessarily make sense at the speed at which you can read and understand non-math), then skim/skip to the next lay portion. Depending on how you feel with that, you should look at the math parts (the .2s) which will look familiar if you were able to finish the lay sections. I can’t promise they’ll make sense, but things should be vaguely readable. Maybe. The weeds (the .3s) contain extra information (some lay, some math) and calculations, more for answering questions than for reading. Enter at your own peril.

1.1.2 The Initiated

Welcome mathy friend! Depending on the extent of your initiation (and your sense of humor), this thesis may be exactly what you’ve always wanted to read! Skim the laysplanations (.1s), but if they are too math-less for you, it’s okay to only read the math sections (.2s) and just go back to the lay stuff if necessary (several things are introduced/motivated in the laysplanations, including explanations of my Formula in the .1.1s). You may also be interested in the weeds (.3s) which are appendices with things that weren’t strictly necessary to get through the proof of the Main Theorem, but were necessary personally for me to get a hold of things. The weeds aren’t to be read straight through, but you might find an explicit calculation or extra explanation there.

1.1.3 The Mathematician

Dear Professor, thank you for showing interest in my thesis! Your introduction awaits at §1.3. For results, however, you may find the fluffless arxived original [BH13] easier to read (certainly quicker!) than this thesis.

The naive short answer is: Infinitely many! But of course, though true, that is not nearly enough information. What we will show is that the infinitely many shapes we find are actually “equidistributed” with respect to the “space of shapes.” In other words, if you think of the collection of possible shapes as being a blob (a “space”), then wherever you look in this blob, you will find shapes of number fields in equal quantity.

Equivalently, though somewhat less to my liking, a thesis is a claim and a (very long) proof. My equivalent claim in layspeak is: “Shapes” of certain degree n “number fields” become “equidistributed” when ordered by “absolute discriminant.”

In what follows I hope to do enough “laysplanations” to make the whole argument approximately readable by approximately anyone. Approximately. In addition to laysplaining and “mathsplaining,” I will also, where appropriate and not too horrifying, have some “weedsplanations” where I wade into the weeds with examples and explicit calculations, sometimes with extra laysplanations that were not strictly necessary to the main argument.

People often say kids are natural scientists. It isn't true, but they have bushels of curiosity and that is a key component of science and math. Somehow this goes away in somewhere around the 5th grade. It shouldn't be - perhaps it is useful to look at where STEM education came from.

With the cold war came a recognition that the country needed scientists, engineers and mathematicians in much greater numbers than ever before. The curriculum was changed to ensure that a pipeline was created to identify and nurture those who would ultimately end up with Ph.D.s from the best universities in the country and programs within the universities were greatly expanded. In two decades the number of physics Ph.Ds. increased from under 200 to about 800 a year. There was this one little problem. What do you do with the millions of people outside the pipeline?

There is a deeply rooted assumption that science literacy is good for society. That somehow the pre and pre-pre professional courses designed by Berkeley and MIT would create a citizenry that could deal with science and society issues. Unfortunately there isn't any empirical evidence to support the assumption.

Just how do people interact with science? About ten years ago stem cell research was a hot topic in the news. There were diverse group. People with parents who have Alzheimer's, certain fundamentalist Christian sect members and biotech investors were some of the groups with differing motivations driving their interests. Global warming is another example - depending how you cut it there are at least a half dozen distinct groups (I have some nasty scars on this one). And now we need to strap in for CRISPR. Science and the public issues are important, but the reality is we have many publics each with their own issues.

Another huge issue is science is not a single monolithic subject. Science education teaches about the scientific method. Science doesn't work like that - reality turns out to be a different beast. Scientists agree on hypothesis testing and many methods, varying across branches and subpecalities. Trying to sort out the methodological differences between black-footed ferrets studies, climate modeling, and theoretical particle physics is a non-trivial task to anyone outside of science.

Most people don't worry about science on a regular basis but rather when something comes up and they would like to use it. Your two year old is showing signs of autism, your tap water has so much natural gas in it that you can set it on fire, the license on the nuclear power station twenty miles away is up for renewal, you are worried about losing weight and eating better... Text book learning isn't terribly useful and pronouncements by experts and pundits are often at odds. What is taught involves a regurgitation of memorized "facts" and the ability to plug in some numbers into equations to answer an artificial problem set. You have learned this thing science so you can score well on standardized tests. Generally people have little ability, five years out of school, to form a meaningful question and come up with a reasoned path that might be useful. We need to teach a useful science literacy. I was going to add an aesthetic science (and math) literacy, but I think that comes with study.

I was very lucky in high school. It was a time and place where some of the teachers were allowed to create their own courses on their own. Not every class, but a few were enough to keep me excited. My two best teachers taught history courses. Neither taught a bag of places or dates that we had to recite and as such that probably didn't help us on standardized tests. One had classroom discussions, both lectured and both required papers every few weeks on a topic or two of your own choice. They were trying to get us to understand history in context and to relate it to the present - which happened to be a very spooky time. I still can't remember dates and places well, but I think I have a better appreciation for the flow of history than the average high school graduate - enough that it helps me think about societal issues and begin to work out how to think about politics and policy. Again - I wouldn't claim to be great at it, but the education I had was much deeper. Had it not been for some native curiosity and some out-of-school mentoring I probably would have thought about majoring in history. (and that may have been good)

The good news is people are experimenting with programs that allow students to find and interpret science in the context of real world problems as well as judge the credibility of scientific claims. Courses like these may need to find interests of the student that can be used to apply science and this may lead to paths far from what is currently measured in standardized tests. There are barriers to be broken, but it is exciting to contemplate a much larger population that has a bit of real science literacy rather than the current artifact of pipelining. Some exciting work is going on: Problem-Based Learning, Place-Based Education, Science-Technology-Society approaches and probably a dozen I'm not aware of.

In college we have examples like Piper's thesis. I think physics and astronomy are in better shape, but more needs to be done. And outside of formal education the seeds being planted with laysplaining from YouTubers like Physics Girl and Minute Physics are just.plain.wonderful!

° grate the zest from the lemon and then mix with the parsley and set aside

° bring a large pan of salted water to a boil, add the spaghetti and cook until al dente.

° in a large pan, gently warm the olive oil, garlic and chilli over a low flame until fragrant – do not let it burn.

° once the spaghetti is cooked, use a sieve or tongs to lift the spaghetti and a just a little residual water into the frying pan. Stir, add the lemon and parsley, a pinch of salt and if you like a squeeze of lemon, stir again,

12/28/2015

With that he reached into his coat pocket and handed me a screwdriver. I had only met my director once before during the job interview, but here we were in one of the elevators at Bell Labs in Murray Hill about to hack said elevator. A bit of fiddling and the panel was off. He had closed the door and was lighting a small butane powered soldering iron. Friedolf was a known instrumentation expert - a breed as interested in how something is measured as the physics it is after. He made his reputation measuring hydrogen bomb blasts. How much can you accurately measure before your instruments are destroyed. These guys are astonishingly good with physical signals. In under three minutes the panel had been replaced. Spliced into the wiring was an empty connector. We stopped off at the stock room for a few 7400 series ICs and other bits and pieces.

He had worked out the simple logic of the elevator control during an hour of play the day before. The idea was to install a simple state machine - a primitive computer of sorts - that would change the requested floor every once and awhile. Every ten or so trips the elevator indicator would show where the rider intended to go, but bit of kit we installed early the next morning would redirect it to a different floor. We could adjust the period between redirects. It was an excellent introduction to the culture of the place.

A few months in and he called me into his office.

You're working too hard. Why don't you take a week or two off from what you've been doing. Find something interesting to work on. Something different from anything you've worked on or thought of working on. You're not going to learn much in a week, but if you're lucky maybe something will connect in your head. All I ask is you throw yourself into it and tell me about it in a month or two.1

These mini-Sabbaticals generally took place early in January. They continued for a decade until I moved to a different lab and assumed most people were doing something like this. In fact more than a few people created their own paths as part of their research direction - I certainly did - but the instruction to do something very different wasn't as common. My new director called me in and told me about a note describing the week long explorations suggesting it would be important that I stay with it as it had paid off.2 The same note made its way to the third director with the recommendation of the second. After leaving AT&T Research I maintained the tradition. I had made too many connections to different people and fields to give up. While my formal education and much of my work was extremely focused, I had found a mechanism for spreading out and finding a few new dots to connect. It had become something of a serendipity generator. All I have to do is be smart enough to wire in a bit of the new for a new perspective and vision. I'm pretty sure it has made me better at what I do and even how I think.

The 30th of December approaches. That's the day I choose the subject.

__________

1 This is a rough quote

2 This was remarkable as the divestiture was taking its toll on pure research and the Labs was now business focused. Much has been written on the subject, but the organization and company were poorly suited a competitive world outside the protection of regulated monopoly. The end of an era - that kind of research is very rare these days. But good work is being done in some of government and university labs.

__________

Recipe Corner

Most of the Christmas cooking consisted of old favorites. I did try a few recipes others suggested. This one is excellent - I used dried cranberries rather than raisins and very good heritage carrots. I'm back to playing with the food and the next post should see something different.